Federal prosecutors have issued sweeping subpoenas demanding that millions of North Carolina voter records be turned over to immigration authorities by Sept. 25.

With just two months to go before the midterms, the subpoenas threatened to sow chaos in the state’s election machinery, while renewing the Trump administration’s repeatedly discredited claims of widespread voting by illegal immigrants.

The unsealed grand jury subpoenas were sent to the state elections board and to 44 county elections boards in eastern North Carolina. Their existence became widely known after Marc E. Elias, a voting rights lawyer aligned with the Democratic Party, mentioned them on Twitter.

Though the nature, scope and impetus of the federal investigation that generated the subpoenas remain shrouded in mystery, the move appeared to be part of an effort to find and crack down on any unauthorized voting by noncitizens.

Representatives of ICE and the Justice Department officials involved declined to comment on the matter.

The subpoenas were issued on Friday, a week after federal officials announced that 19 noncitizens in North Carolina had been charged with casting illegal votes in the 2016 election. Those indictments arose from an investigation by a newly created federal task force focused on document and benefits fraud in the Eastern District of North Carolina, where the 44 counties are.

Critics say that those arrests hardly constitute a wave of voter fraud worthy of such a broad demand for documents, which they said could overwhelm the budgets and staffs of small counties just when they need to be preparing for the November election. And they raised concerns about privacy: Among the prosecutors’ demands are millions of secret ballots cast by absentee and early voters whose identities could be easily traced.

Some critics also speculated that the Trump administration was looking to continue the work of its much-maligned voter fraud commission, which was disbanded in January in a blizzard of complaints and litigation after finding no evidence of significant fraud or a corrupt voting system.

It was the latest in a series of controversies surrounding the question of voter fraud, and whether Republican-backed efforts to combat it mask an effort to actually suppress voter turnout.

North Carolina has had more of these controversies than most states. In 2016, a federal appeals court struck down a state voter identification law written by North Carolina Republicans, saying that it was aimed at African-American voters “with almost surgical precision.” On Election Day this year, voters will consider a Republican-backed constitutional amendment that would require voters to show a photo ID at the polls.

The state elections board audited the 2016 election and reported in April 2017 that it had found 41 suspected cases of noncitizens casting votes.

President Trump has nonetheless called the American voting system “rigged,” and has frequently made unsupported claims that millions of people, including many undocumented immigrants, have been voting illegally.

When the Trump administration’s voter fraud commission imploded in January, the commission’s vice chairman — Kris Kobach, the Kansas secretary of state — said its work would be transferred to the Homeland Security Department; ICE is part of that department.

Bryan D. Cox, an ICE spokesman, said on Wednesday that the investigation in North Carolina was “locally driven” by the office of the United States attorney for the Eastern District, Robert J. Higdon Jr.

In previous administrations, United States attorneys routinely sought approval from senior Justice Department officials before undertaking investigations that were likely to attract national attention or cause controversy, according to Vanita Gupta, who led the department’s Civil Rights Division under President Obama. “Given its atypical nature, it’s hard to imagine that main Justice was unaware” of the investigations and the subpoenas, she said.

A Justice Department official in Washington referred questions about the matter to Mr. Higdon’s office, which declined to comment.

Allison Riggs, a lawyer with the Southern Coalition for Social Justice, wondered whether the subpoenas were part of the next chapter that Mr. Kobach had promised for the voter fraud effort.

“This is clearly a fishing expedition that picks up where the Pence-Kobach Commission stopped,” said Ms. Riggs, referring to Vice President Mike Pence, who had been chairman of the commission. Ms. Riggs added that the administration “appears to be outsourcing the Commission’s discredited agenda” to federal prosecutors.

“Nothing about it is normal,” said Ms. Gupta, who is now president of the Leadership Conference on Civil and Human Rights. “It asks for information that has nothing to do with identifying immigration violations.”

To some voting rights advocates, the subpoenas recalled a long campaign by the Justice Department under President George W. Bush to find and prosecute cases of voter fraud. United States attorneys who refused or failed to devote time to the comparatively low-level voter fraud cases were dismissed under political pressure. By its end, the campaign had secured just 86 convictions, including some that were suspect, out of more than 200 million ballots that had been cast.

‘The Trump administration has made the idea of voter fraud a big rallying point,” said Myrna Perez, the deputy director of the democracy program at the Brennan Center for Justice at the New York University School of Law. “It’s a common refrain by political actors who find it advantageous.”

She and others noted that starting a sweeping voter fraud inquiry so close to a crucial election could depress turnout, not only by naturalized immigrants who can vote legally but also by other groups who may distrust the government.

Many of the 19 people charged last month were nonwhite, Ms. Perez said, and a number said in interviews that they were unaware that they did not have the right to vote. Many of the 44 counties that received subpoenas have populations that are disproportionately poor and black.

The subpoena to the state elections board requests documents from 2010 through August 2018, including voter registration applications, early voting application forms, and absentee ballot request forms.

Joshua Lawson, general counsel for the North Carolina State Board of Elections and Ethics Enforcement, estimated that it covered more than 15 million state documents.

The subpoena to the county boards requests “any and all poll books, e-poll books, voting records, and/or voter authorization documents and executed official ballots” for a five-year period beginning Aug. 30, 2013.

Mr. Lawson said that this would cover in excess of five million county documents.

The subpoena request, he said, was “probably the largest on record in North Carolina within our agency.” He, like others, said he was puzzled by the investigation’s goals.

“With the scope so broad, what is the particular interest of immigration authorities?” he said.

The state elections board plans to consider the subpoenas in a telephone meeting on Friday, and may discuss whether to resist them.

Mr. Lawson said he had written to the county boards, advising them to contact Mr. Higdon’s office directly if they wanted to ask for an extension of the Sept. 25 deadline. Sebastian Kielmanovich, an assistant United States attorney, told Mr. Lawson in an email that such requests would be considered “upon execution of a document to be provided committing to preserve/not destroy the requested information.”

Mr. Lawson had told Mr. Kielmanovich that his office was “deeply concerned by the administrative drain” counties would suffer from complying with the subpoenas. In an interview, Mr. Lawson said that the counties would have to scan millions of paper ballots.

In rural Nash County, John Kearney, director of the local elections board, said that producing records of past elections would be an overwhelming task for the board’s three clerks. “We’re going to have to have an extension, and call in a contractor with high-speed copiers to do it,” he said. “We don’t have the manpower or time in this small office.”

Of particular concern was the subpoena’s request for actual ballots that had been cast in prior elections. In North Carolina, votes cast on Election Day are anonymous and untraceable, but absentee ballots and those cast in early voting — a sizable share of the total — are marked with numbers that can be traced to the people who cast them.

Some election officials said they were unsettled at the prospect of handing over traceable ballots to federal prosecutors, and believed that their counties’ voters would be as well.

“I thought it was a hoax when I got it,” said Kellie Hopkins, the director of the elections board in Beaufort County. “A subpoena for ballots? I’d think they’d understand you don’t give out ballots.”

Ms. Hopkins said her office could produce computerized records showing which registered voters cast ballots in elections dating back several years. But she said the county board would meet this week to consider whether to turn over actual ballots.

Both she and Mr. Kearney said they worried that the subpoenas could further erode voters’ already low confidence in election security, and perhaps depress turnout in November as well.

“Most voters expect privacy when they come to the board of elections to vote,” Mr. Kearney said. “When this information gets out, and it will, voters are going to be upset that their ballots and the names tied to them are being given to a federal prosecutor.”

Privacy concerns also dogged Mr. Trump’s commission. A number of states refused to give the panel information it requested because it contained personal data about voters.

Ms. Riggs said that in normal circumstances, North Carolina law prohibits the release of private voter information like dates of birth or the last four digits of social security numbers, which can be found on documents like voter registration applications.

But she said she did not know how state law would apply in the face of a federal subpoena.